Suppression of the spectral narrowing effect in lasers mode-locked by saturable absorbers

Volume 8, number 1

OPTICS COMMUNICATIONS

May 1973

SUPPRESSION OF THE SPECTRAL NARROWING IN LASERS MODE-LOCKED

BY SATURABLE

EFFECT

ABSORBERS

D. VON DER LINDE and K.F. RODGERS

Bell Laboratories, Murray Hill, New Jersey 07974, USA Received 26 March 1973

A gain profile with a very flat top is produced by incorporating a Fabry-Pdrot interferometer in the cavity of a mode-locked Nd-glass laser. With proper adjustment of the interferometer parameters, the spectral narrowing effect is significantly reduced, and bandwidth-limited pulses as short as 1.5 psec have been observed.

Recently it has been shown that at low power density (<~ 300 MW/cm 2) mode-locked pulses generated by Nd-glass lasers are bandwidth limited [1]. The pulse duration was found to be typically 5 to 6 psec. The corresponding frequency width Au ~ 3 to 4 cm 1 is only a very small fraction of the gain bandwidth in Nd-glass, Aug ~ 200 cm -1. In view of this broad bandwidth, it should be possible to generate very much shorter pulses with Nd-glass lasers. A first step towards this goal should utilize the gain bandwidth more effectively. The formation of ultrashort light pulses starts from very short random intensity fluctuations. At the beginning of the generation the duration "rfl of the fluctuation is given by the inverse width o f the spectrum of the excited (randomly phased) modes, i.e., 7"fl ~ (AUg) -1. During the linear amplification regime [2] the modes in the wing of the gain band grow much slower than the modes close to the center. The resulting rate of spectral narrowing [3] depends on the curvature of the gain band at the center. The significance of the spectral narrowing for the duration and frequency width of the final pulses has been noted in the literature [2]. The purpose of this paper is to describe a technique tbr partial suppression of spectral narrowing. The curvature of the effect gain band of the laser is minimized using a Fabry-P6rot interferometer inside the laser cavity. A similar method has been suggested by Letokhov [2]. Consider the build up of power in a laser shown

schematically in fig. 1, Let Pk(u) denote the power spectrum at the end of the kth cavity round-trip. Then the power spectrum after one more round-trip is given by

Pk+l(V) = Pk(v) F2(v),

(1 a)

Ft(u ) = (R1R2)1/2 T A G(v) T(v) ~

(1 b)

Here T(v) is the single pass transmission of the F a b r y Pdrot filter, FP, and G(v) is the single pass gain of the laser medium, LM. It is assumed that the reflectivity of the mirrors, R 1 and R2, and the unsaturated transmission T A of the absorber, A, are independent of frequency, e.g., the frequency dependence is considered to be absorbed in the gain function, G(v). The transmission of the Fabry-Pe'rot is given by

T(v) = {1 +~F[l+cos(Zn(v pl)/APl)]} -1 ,

(2)

where Av 1 = c(2dcosO) -1. F i s the finesse; d is the spacing of the two surfaces that form the interferometer; 0 is the angle of incidence (see fig. 1). The

LI' RI

A

' LM

\\ FP

U R2

Fig. 1. Schematic of the laser: mirrors, R 1 and R2; saturable absorber, A; laser medium, LM; Fabry-Pe'rot interferometer, FP, with angle of incidence 0, and spacing d. 91

Volume 8, number 1

OPTICS COMMUNICATIONS

May 1973

F a b r y - P6rot has a minimum of transmission at v = Pl" 0.2

The gain function may be written

G(v) = e x p { g 0 e x p [ - ( ( v

Vo)/AVg)2 ]}.

(3)

exp(g0) is the single pass gain at the center of the gain band, and Aug is the bandwidth. The assumption of a gaussian shaped band is not crucial. To effectively reduce the spectral narrowing it is required that (i) the gain maximum coincides with the transmission minimum Pl = Uo, and (ii) the curvature o f F t is zero at v0: dZFt(v)/dv2lv=vo = 0. The first condition is satisfied if

Av 1 = c(2dcosO)

1 = (2/m)v 0 ,

(4)

where rn is an odd integer. The second condition leads to

Av 1 = AVg[ (rr2 /go) F / ( F +

Av n = 2[(2n/4[ In 2) d4Ft(v)/dv4 [v=vo] 1/4,

(6)

where use has been made of the relation d2Ft/dv2 = O. A similar expression for the frequency width in the absence of a F a b r y - P ~ r o t can be obtained by replaci n g ( F + 1) -1 for T(v) in eq. (6). It is interesting to compare the frequency width with a compensating F a b w - P d r o t and the width without F a b r y - P d r o t for otherwise the same condition. The ratio r of the widths is found to be lln2[(l+b~l)/3-(g0+l)/2g0]}

'1/4.

(7)

In a laser with a saturable absorber it takes a few thousand round trips for the light to reach a power level where the biggest fluctuation starts to bleach the absorber [2,4]. For a single pass gain exp(g0) = 2.34, a finesse F = 0.1736 (two uncoated glass surfaces at normal incidence), and n = 2500, eq. (7) gives r ~ 8.9. This implies that at the onset of absorber bleaching the intensity fluctuations are about 8.9 times shorter than in a laser without the Fabry Pe'rot, and with a sufficiently fast recovering absorber the final output pulses will be shorter by approximately this factor r*. 92

/

O.I

J

,! ! i i i i

-0.~

/

%_

S

~3 0

/

I

I

2

3

0 [0EGREES]

I i I

Fig. 2. Normalized width (solid curve) and position (dashed curve) of the frequency spectrum versus Fabry--P~rot angle of incidence. Avg ~ 140 cm -1.

(5)

1)] 1/2 .

Since the finesse F depends on the angle of incidence 0, it is possible to satisfy eq. (4) and eq. (5) simultaneously for different values of m. If the frequency width Av n after n round-trips is small compared to the initial width Av 0 ~ Aug, then Av n is approximately given by

r={(2n)

a=,

Fig. 2 shows the dependence of the width Av and the position v o f the generated frequency spectrum. The same parameters as in the numerical example above have been used. It is assumed that perfect matching is obtained close to normal incidence, 0mi n = 1°. As 0 is increased, the laser line is tuned tohigher frequencies and the spectral width decreases quite rapidly. At 0 ~ 0mi n + 0.1 ° [corresponding to (v 1 Vo)/Av 1 ~ 2 X 10 - 3 ] A v h a s dropped to approximately half the maximum value. Eq. (5) is somewhat less critical. Imperfect compensation of the gain band curvature, say ( d 2 F t / d v 2 ) ( d 2 G / d v 2 ) -1 ~ 5 X 10 - 2 decreases Av to one half of the width for perfect matching. Experiments were performed with an Nd-glass laser mode-locked by Kodak dye 9860. The F a b r y P~rot consisted of two plane wedged quartz fiats. Metal foil spacers provided a plane parallel air space of approximately 30/~m. A precision mount allowed control of the angle of incidence 0 with an accuracy better than 2.5 X 10 _`2 degrees. The frequency spectra were measured with a grating spectrometer and calibrated photographic plates. The time structure of the generated pulses was studied using the two-photon fluorescence method [5]. First, the frequency spectrum of the mode-locked * Further pulse shortening occurs when the peak intensity is comparable with the absorber saturation intensity.

Volume 8, number 1

OPTICS COMMUNICATIONS

pulses was measured as a function of 0. The spectra followed very closely the behavior predicted by fig. 2. As 0 approached 0rain, the laser line moved close to the center of the gain band at v0, and distinct line broadening occurred, as expected. It is important to emphasize the different character of the frequency spectra generated with the help of the Fabry-P~rot and the spectra observed when nonlinear broadening was operative. At higher power densities ( ~ 1 GW/ cm 2) the spectral width is in excess of 50 cm -1 and most of the spectral energy resides in the wings of the distribution. Unlike these spectra, characteristic of nonlinear frequency broadening, frequency spectra with very steep wings were measured at low power with a carefully matched Fabry-Pgrot. A typical experimental spectrum is shown in fig. 3 (solid curve). The half-width of this spectrum is Av ~ 20 cm -1 and the width at llY/~ of the maximum is 36 cm -1. For comparison, the dashed curve in fig. 3 shows a typical high-power spectrum with a 10% width of approximately 200 cm -1. Two-photon fluorescence (TPF) experiments performed simultaneously with the spectral measurements indicated that the pulse duration agreed well with the inverse frequency width. On the average with an accurately matched Fabry-Pdrot, the frequency width was 10 to 1:5 cm -1. The TPF indicated pulses of 2 to 3 psec duration. The best results were pulses of 1.5 psec having a bandwidth-limited frequency spectrum of 20 cm -1. It is well known that the interpretation of TPF experiments requires some caution because of the am-

biguity of the autocorrelation function [6]. Primarily, the experiments have shown that intensity fluctuations of much shorter duration can be sustained during the linear regime of pulse generation. Whether these short fluctuations can be transformed into welldefined isolated short pulses depends on the ratio of the recovery time r of the absorber to the duration of the fluctuations, "rfl. In the present experiments, we have r ~ 7 psec and Tfl ~ 2 psec (7/7fl ~ 3.5). The effect of finite absorber relaxation time has been investigated experimentally on a nanosecond time scale [4]. For 7-/Tfl similar to our value the output occasionally consisted of a peak of duration rp ~ 7fl accompanied by approximately r/rfl weaker components (see fig. 8 of ref. [4]). These observations suggest that the pulses in our experiment (picosecond time scale) have a similar structure. However, the measured TPF traces in most cases did not exhibit a distinct shoulder or secondary peaks, expected when a group of pulses is measured instead of a single pulse [7]. This finding can be explained by the statistical character of the appearance of fluctuations of comparable size within a time interval r. In conclusion, it has been shown that the spectral narrowing during the linear regime of the generation in a dye mode-locked laser can be effectively suppressed with the help of a matched Fabry-Pdrot. The experimental results confirm that very short intensity fluctuations are responsible for the formation of ultrashort light pulses in these lasers. With the availability of faster recovering saturable absorbers, the system described in this paper is very promising for the generation of light pulses of 10 -12 sec duration and less. The authors gratefully acknowledge usethl discussions with J.R. Klauder.

i.O ~

/ 0.5

,,/

,,

/

\

i ~"

-6o

May 1973

-45

-3o

References

",,,,, %.

-~

o

~5

30

45

6o

(x-x o) [~,] Fig. 3. Measured frequency spectra: low power with compensating Fabry-Pe'rot (solid curve). The dashed curve shows a spectrum measured at very high power.

[ 1] D. vonder Linde, IEEE J. Quantum Electron. QE-8 (1972) 328; N.G. Basov et al., FIAN Preprint No. 82 (1972). [2] V.S. Letokhov, Soviet Phys. JETP 28 (1969) 562; J.A. Fleck, Phys. Rev. 1A (1970) 84. [3] W.R. Sooy, Appl. Phys. Letters 7 (1965) 36. [4] P.G. Kryukov and V.S. Letokhov, IEEE J. Quantum Electron. QE-8 (1972) 766.

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Volume 8, number 1

OPTICS COMMUNICATIONS

[5] J.A. Giordmaine, P.M. Rentzepis, S.L. Shapiro and K.W. Wecht, Appl. Phys. Letters 11 (1967) 216. [6] J.R. Klauder, M.A. Duguay, J.A. Giordmaine and S.I. Shapiro, Appl. Phys. Letters 15 (1968) 174; M.P. Weber, Phys. Letters 27A (1968) 321.

[7] T.I. Kuznetsova, Soviet Phys. JETP 28 (1969) 1303; R.A. Fisher and J.A. Fleck, Appl. Phys. Letters 15 (1969) 287; R.M. Picard and P. Schweitzer, Phys. Rev. l (1970) 1803.

ERRATUM K. Matsuda, J. Tsujiuchi and H. Tanigawa, Coherence in holographic interference of equal inclination, Opt. Commun. 6 (1972) 1 1 1. Mechanical Engineering Laboratory, T o k y o Institute of Technology, O-Okayama, Meguro-ku, Tokyo, Japan on p. 1 11 should read Mechanical Engineering Laboratory, 4 12, Igusa, Suginami-ku, Tokyo, Japan. In fig. 1 on p. 111, x 0 and Y0 should read x and y, respectively. Infig. 6 o n p . 113,

~. (ai,a}), Yl[IAil2+ t a(x,y) •

a'*(x,y),

a* (x,y) • a'(x,y),

94

May 1973

IAII 2] and ~ (ai*a~) should read i F - I [ I A ( ~ , ~ ) I 2 + iA'(~,~)l 2] and

respectively.